The present invention relates to the field of dynamic system control. More specifically, one embodiment of the invention allows for controlling systems with multiple, interacting inputs and outputs using non-interacting single-input single-output tunable controllers and techniques, while accounting for the interacting nature of the system being controlled and adapting to system variations.
Control systems are used in a wide variety of fields, such as industrial processes, environmental systems, electronic systems, and any other system where system output variables representing measurements and user specified desired outputs ("process variables") are processed to generate system input variables which control devices which change the system. A simple example of a control system is a heating and air conditioning ("H/AC") system. There, the controller inputs may be the temperatures of the rooms being controlled and a thermostat setting. The controller outputs may be air flow (volume/time), temperature of outgoing air, power setting of a compressor, etc. The goal of the control system is to regulate the temperature in each room being controlled to the thermostat setting for that room. If the rooms are not coupled (via open doors or the like), each room can be treated as a single-input (air flow) and single output (temperature) system. However, where the rooms are coupled, the control solution must be a multi-input multi-output controller to account for the interactions between rooms.
Fundamental to the use and effectiveness of any controller is its ability to regulate the process outputs of the system being controlled to reject disturbances, to maintain stability and performance specifications in the event of system variations, and to minimize the effort and time required for tuning the controller's performance. Tuning is the process of setting the controller's internal logic, circuitry and/or variables so that the controller's output signals cause the desired effect (of reaching the controller's goal) given the controller's inputs.
Single-input single-output (SISO) controllers are simpler to tune than MIMO controllers, but SISO controllers cannot account for control of processes with multiple interacting inputs and outputs. Multivariable control techniques can account for all the interactions between the process variables by utilizing a dynamic model of the process, but require a dynamic process model development and a non-generic, manual design, which cannot be generalized easily, for each multivariable process considered.
Detailed studies of multivariable feedback control design are found in J. Doyle et al., "Multivariable Feedback Design: Concepts for a Classical/Modern Synthesis," IEEE Transactions on Automatic Control, vol. AC-26, No. 1 (February 1981), J. Maciejowski, Multivariable Feedback Design, Addison-Wesley (England 1989) (hereinafter "Maciejowski") and K. Ogata, Discrete-Time Control Systems, Prentice-Hall (New Jersey 1987) (hereinafter "Ogata"). These references are incorporated herein by reference for all purposes.
The types of control synthesis techniques described in those references are "model-based" techniques in that they rely on a dynamic model to shape cost functionals or a magnitude curve to achieve certain performance objectives. The model-based synthesis process requires an in-depth knowledge of these techniques and significant numerical computation, a consequently it does not lend itself to easy on-line tuning. The necessary calculations are quite involved, are not always numerically stable or robust, and may not be feasible in all cases to implement on-line. Although these model-based techniques are powerful tools for synthesizing control algorithms and can achieve excellent performance on many applications, they are not suited to be made into a generic, easily tunable structure which can be designed without being limited to a particular example of a controlled system or a system known in advance. Model-based techniques are more suited for custom designs by those with significant skill in designing control systems.
One approach which partially solves the foregoing problems is the use of the Inverse Nyquist Array (INA) and Characteristic Loci (CL) methodologies. For a detailed description of these methodologies, see Maciejowski. Those methodologies are multivariable generalizations of the SISO Nyquist theory and root-locus design techniques which attempt to transform a coupled process into smaller design problems, but those methodologies are still complex to use and understand. Both INA and CL require a process model and in most cases must be used off-line (i.e., cannot be used in real-time). INA and CL attempt, with pre-compensation and post-compensation, to achieve a diagonally dominant system over the entire frequency range of the system. This leads to difficulties in the realization of the controller; it cannot be physically realized or built because it violates causality (i.e., it depends on signals before the signals exist.) With INA and CL techniques, as with the other model-based techniques previously mentioned, there is no direct way to tune the controller's performance on-line. Another limitation of INA and CL is that, while they do allow for the design of scalar problems, they concentrate on SISO reliability (robustness), to the detriment of MIMO reliability.
From the above it is seen that a gap exists between easily tunable, non-interacting SISO control techniques and interacting, difficult to tune MIMO techniques, resulting in dichotomies in use and performance. What is needed is a non-interacting dynamic controller which accounts for the interactions in a MIMO dynamic process.